Get the Short Domain Name
CMD: echo %userdomain%
Powershell: gci env:userdomain
Get the Domain
From an elevated prompt (cmd or powershell)
nltest /parentdomain
Get Domain Controller
From an elevated prompt (cmd or powershell)
nltest /dsgetdc:<DOMAINNAME>
Ex: nltest /dsgetdc:foray.local
For other methods, see: Find Name of the Active Directory Domain Controller.
Test Domain Membership (Trust Relationship)
netdom verify <Computer>
Ex: netdom verify MYPC
See also: Check Domain Trust Relationship